Entanglement is not enough
Open accessAbstract
This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the quantitative calculations that form the basis of the arguments.
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The wormhole is getting longer.
“This is the fact that the wormhole is getting longer [62, 63].”
From Replica wormholes and the entropy of Hawking radiation (2020) · cites this paper as [63]
The entropy of region R without considering the island grows linearly with time t_b, S_Hawking ∼ πc/(6β) t_b.
“The entropy of region R without considering the island grows linearly with time t b , S Hawking ∼ πc 6β t b .”
From Replica wormholes for an evaporating 2D black hole (2021) · cites this paper as [69]
Section 2.1 (page unavailable) discusses Hawking emission, while section 3.3 describes a global entropy assigned to Einstein–Rosen-bridge causal patches. Neither gives the entropy of a radiation region R without an island or the claimed πc/(6β) growth rate; searches for those terms and for radiation-entropy growth found no matching passage. (LLM, conf=0.76)
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Spectral and Krylov complexity in billiard systems
Camargo, H. A., Jahnke, V., Jeong, H.-S., Keun-young Kim, A., & Nishida, M. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.046017 · Cited by 51 · see citing works
Bosonic and fermionic Gaussian states from Kähler structures
Hackl, L., & Eugenio Bianchi, A. (2021) · SciPost Physics Core · doi:10.21468/scipostphyscore.4.3.025 · Cited by 50 · see citing works
Quantum complexity in gravity, quantum field theory, and quantum information science
Baiguera, S., Balasubramanian, V., Caputa, P., Chapman, S., Haferkamp, J., Heller, M. P., & Halpern, N. Y. (2025) · Physics Reports · doi:10.1016/j.physrep.2025.11.001 · Cited by 57 · see citing works
Testing holographic conjectures of complexity with Born–Infeld black holes
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Complexity and action for warped AdS black holes
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A complexity/fidelity susceptibility g-theorem for AdS3/BCFT2
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Holographic spacetimes as quantum circuits of path-integrations
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C${\cal C}$osmological K${\cal K}$rylov C${\cal C}$omplexity
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More on complexity of operators in quantum field theory
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EPR pairs, local projections and quantum teleportation in holography
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Quantum criticality and state engineering in the simulated anisotropic quantum Rabi model
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Probing the entanglement of operator growth
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Lorentzian Threads as Gatelines and Holographic Complexity
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WdW-patches in AdS3 and complexity change under conformal transformations II
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Holographic complexity in dSd+1
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Circuit complexity and 2D bosonisation
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Complexity of mixed Gaussian states from Fisher information geometry
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Bath deformations, islands, and holographic complexity
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Does boundary distinguish complexities?
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Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories
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Complexity from the reduced density matrix: a new diagnostic for chaos
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EPR pairs, local projections and quantum teleportation in holography
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Partial islands and subregion complexity in geometric secret-sharing model
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Holographic complexity of quantum black holes
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- Authors
- Susskind, L.
- Affiliations
- Stanford University (US)
- Corresponding author
- Susskind, Leonard
- ORCID
- Susskind, Leonard
- Venue
- Fortschritte der Physik
- Publisher
- Wiley
- Published
- 2016-01
- Volume
- 64
- Issue
- 1
- Pages
- 49-71
- ISSN
- 0015-8208 (ISSN-L)
- 1521-3978
- OpenAlex
- W2162408901
- Cited by
- 427
- References
- 38
- Citations by year
- 2026: 15 · 2025: 31 · 2024: 31 · 2023: 47 · 2022: 49 · 2021: 62 · 2020: 48 · 2019: 52 · 2018: 48 · 2017: 29 · 2016: 11 · 2015: 4
- FWCI
- 22.53
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Fortschritte der Physik (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0756174)
- John Templeton Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- black holes, quantum complexity, quantum entanglement, quantum chaos, black hole information
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